Problem 85 - College Algebra

Question

Perform the indicated operation or operations. $$(5 x-7)(3 x-2)-(4 x-5)(6 x-1)$$

Step-by-Step Solution

Answer

-9x^2 + 4x + 9

Step 1: Distribute the Terms

Apply the distributive property (also known as the FOIL method in this case as there are two binomials) to expand each set of parentheses. FOIL stands for First, Outer, Inner, and Last, which refers to the terms you are multiplying together in each binomials. For the first term this results in \(5x * 3x + 5x * -2 + -7 * 3x + -7 * -2\) which simplifies to \(15x^2 -10x - 21x +14\). Similarly, for the second term this results in \(4x * 6x + 4x * -1 + -5 * 6x + -5 * -1\) which simplifies to \(24x^2 -4x - 30x +5\). This turns the original equation into \((15x^2 -10x - 21x +14) - (24x^2 -4x - 30x +5)\).

Step 2: Subtract the Terms

Now, subtract the terms from the second parentheses from the terms in the first parentheses, resulting in \(15x^2 - 24x^2 + -10x + 4x - 21x + 30x +14 - 5\), which simplifies to \(-9x^2 +4x + 9\).

Step 3: Final Simplified Expression

So, the given exercise after performing the indicated operations simplifies to \(-9x^2 + 4x + 9\).